Spread-time code division multiple access technique with arbitrary spectral shaping

ABSTRACT

A spread-time code division multiple access (ST-CDMA) technique is disclosed for bandlimited access to a channel. With ST-CDMA, pseudo-random (PN) sequences are assigned to each transmitter in the multi-transmitter system, and the Fourier transform of the transmitter pulse for a given transmitter is determined by modulating the phase of the desired transmitter spectrum by the PN Sequence assigned to the transmitter. The data symbols produced by the transmitter are conveyed by delayed versions of the transmitter pulse. The transmitted data for a particular transmitter is recovered at a receiver synchronized to the transmitter by sampling the output of a filter matched to the corresponding transmitter pulse.

This is a division of application Ser. No. 07/796,642, filed Nov. 22,1991.

FIELD OF THE INVENTION

This invention relates generally to multi-user digital data transmissionover bandlimited channels and, more particularly, to code divisionmultiple access to the bandlimited channels.

BACKGROUND OF THE INVENTION

The potential demand for ubiquitous wireless communications combinedwith restricted availability of the radio frequency spectrum hasmotivated intense research into bandwidth efficient multiple accessschemes. A recent reference entitled "Spread Spectrum for CommercialCommunications", by Schilling et al, as published in IEEE CommunicationsMagazine, Vol. 29, No. 4, April 1991 discusses one avenue of approach,namely, Spread Spectrum Code Division Multiple Access (SS-CDMA)techniques, to effect multiple access communication.

Conventional CDMA techniques take advantage of available bandwidth onthe transmission medium, such as a fiber optic cable or the radiospectrum, by generating a set of pulses in the time domain which haveappropriate correlation properties over predetermined time periods.Typically, the correlation property is such that a particular receiverturned to a given transmitter code produces a detectable signal wheneverthe given transmitter code is presented to the receiver during each timeperiod, whereas the output of the receiver is near zero for any othertransmitter code presented to the receiver. A CDMA system operating onthis time domain correlation property and utilizing a set of codesdesignated the optimal orthogonal codes was disclosed in U.S. Pat. No.4,779,266.

In the article entitled "Coherent Ultrashort Light Pulse Code-DivisionMultiple Access Communication Systems", appearing in the Journal ofLightwave Technology, by J. A. Salehi, A. M. Weiner, and J. P. Heritage,March, 1990, Vol. 8, No. 3, a technique for encoding a sequence ofultrashort pulses for transmission over an optical channel is disclosed.The encoding is effected by modulating the phase characteristic of theFourier transform of a stream of ultrashort light pulses correspondingto a sequence of data symbols. Each transmitter is assigned a uniquecode to modulate its corresponding stream, and a receiver tuned to thatunique code can detect the data symbols impressed on the short pulses bythe associated transmitter. As disclosed, encoding is accomplished, atoptical frequencies, by an arrangement of grating elements and amultielement phase modulator.

There is no teaching or suggestion in the art of any technique togenerate a transmitter pulse which is power limited and which must matchto a channel having bandwidth restrictions, additive noise, and afrequency transfer response characterized by loss and distortion. Anexample of such a channel is one which supports transmission only ondisconnected frequency bands.

SUMMARY OF THE INVENTION

These shortcomings and other limitations are obviated, in accordancewith the present invention, by assigning a unique code to eachtransmitter, and then by utilizing the unique code to encode thefrequency domain characteristic of a transmitter pulse which is selectedto maximize the overall signal-to-interference ratio at a correspondingreceiver based on the characteristics of the channel interconnecting thetransmitter-receiver pair and additive channel noise.

Broadly speaking, the transmitter from a synchronizedtransmitter-receiver pair propagates, over an interconnecting channel, atransmitted time signal formed with reference to a transmitter pulse.The frequency domain characteristic of the transmitter pulse--designatedthe transmitter characteristic--has both magnitude and phase componentsin the frequency domain. The frequency domain characteristic of thechannel--designated the channel transfer characteristic--also hasmagnitude and phase components in the frequency domain. Given a powerconstraint on the transmitter pulse and given an additive white noise onthe channel, the channel characteristic determines the optimizedtransmitter spectrum (i.e., the square of the magnitude of the frequencydomain characteristic of the transmitter pulse) which maximizes thesignal-to-interference (SIR) ratio at the receiver. The transmittermagnitude, as determined from the spectrum, is modulated by a complexfrequency function having modulus one so that the resultant overallspectrum of the modulated characteristic and the optimized transmitterspectrum are equivalent. The transmitter code is encoded into this phasecomponent so that the transmitter characteristic can be uniquelyidentified at the corresponding receiver. In particular, eachtransmitter is assigned a pseudo-random or pseudo-noise (PN) sequence,that is, the phase component of the complex function can be a squarewave determined by a PN complex-valued sequence. An intermediate timesignal is generated by taking the inverse Fourier Transform of thefrequency domain characteristic obtained by multiplying the transmittermagnitude by the complex function. This intermediate signal is limitedin time by truncating it via time-windowing. The truncated output is thetransmitter pulse, and is the unique time signal associated with thegiven transmitter. Finally, to transmit the actual data informationproduced by a data source associated with each transmitter, periodicallydelayed versions of the transmitter pulse are pulse amplitude modulatedby the actual data information to form the input to the channel, thatis, the transmitted time signal. The delay is the symbol rate.

Broadly, at the receiver, which is synchronized with its correspondingtransmitter via a conventional synchronization technique, the outputtime signal from the channel is time windowed at predetermined timeintervals. The windowed time signal is partitioned into a sequence ofcontiguous time segments, and each of the time segments is processed bytaking its Fourier transmform to obtain a transformed spectrum. Thistransformed spectrum is then modulated by a frequency domain signalwhich is the product of: the transmitter magnitude; the conjugate of thecomplex frequency function; and the conjugate of the channelcharacteristic. The modulator output is processed by a correlationdetector to generate estimates of the data symbols.

This technique of generating the transmitter pulse to match a desiredspectrum is called spread time CDMA. The spread time technique has theadvantage of increasing the flexibility with which power-limited pulsescan be designed with particular spectral characteristics. For example,the transmitter spectrum can have support on disconnected frequencybands, which is relatively difficult to achieve by shaping thetransmitted time signal in spread spectrum systems.

The organization and operation of this invention will be understood froma consideration of the detailed description of the illustrativeembodiment, which follows, when taken in conjunction with theaccompanying drawing.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 depicts a block diagram of the transmitter, including thespectral encoder, to encode a transmitter pulse with a pseudo-noisesequence;

FIG. 2 is an exemplary transmitter pulse for a uniform transmittercharacteristic modulated by a complex function having a pseudo-noisephase characteristic;

FIG. 3 is an alternative transmitter to produce a transmitted timesignal;

FIG. 4 depicts a block diagram of the receiver, including the spectraldecoder, for a synchronized transmitter-receiver pair;

FIG. 5 is an alternative receiver explicitly of the matched-filter type;and

FIG. 6 is a plot of optimized transmitted spectra for an exemplarychannel characteristic.

DETAILED DESCRIPTION Overview of Conventional CDMA

Multiplexing in conventional spread-spectrum CDMA (SS-CDMA) is achievedby assigning a different code, or signature sequence, to eachtransmitter. Each transmitter uses this code to generate a time signalthat can be decoded at a corresponding receiver. To generate a SS-CDMAchannel signal, a time-domain transmitter signal r_(i) (t), typically asingle square pulse of width T, is multiplied by a pseudo-random PNsequence in the time domain. Specifically, it is assumed that thetransmitted time signal for the i^(th) transmitter is of the form##EQU1## where {b_(k).sup.(i) } are the actual information symbolsproduced by transmitter i, r_(i) (t) is the transmitted baseband timesignal assigned to the i^(th) transmitter, and 1/T is the symbol rate.Binary signaling is assumed to apply, i.e., b_(k).sup.(i) ε{±1}. It isdesired that the signals r_(i) (t), i=1, . . . , K, where K is thenumber of transmitters, be nearly orthogonal for all time shifts, thatis, ##EQU2## for all l≠i and τ, where ε is some suitably small constant.In this case the intended receiver can recover the data from itscorresponding transmitter in the presence of interferers by sampling theoutput of a filter matched to r_(i) (t).

Transmitter of the Present Invention

With reference to FIG. 1, there is shown spread-time CDMA (ST-CDMA)transmitter 100 in accordance with the present invention. Transmitter100 for the i^(th) transmitter includes a serial arrangement of:spectrum generator 110; multiplier 120; inverse Fourier transform device130; multiplier 140; and pulse amplitude modulator 150. The output frommultiplier 140, on lead 141, is a transmitter pulse p_(i) (t). Theoutput from stream generator and pulse amplitude modulator (PAM) device150, on lead 151, is the transmitted time signal ##EQU3## produced bymodulating delayed versions of the transmitter pulse with data symbolsprovided by data source 180. Accordingly, device 150 effects generationof a stream of delayed versions of p_(i) (t). The transmitted timesignal on lead 151 serves as the input to channel 50; channel 50 has afrequency domain characteristic designated H(f). Equation (3) is theST-CDMA equivalent to equation (1) for SS-CDMA.

To generate p_(i) (t) in accordance with one illustrative embodiment,spectrum generator 110 produces a frequency characteristic, designatedS(f), on lead 111. The technique for determining the S(f) to be producedby generator 110 is discussed in detail below. Multiplier 120 has as itssecond input, on lead 122, a signal designated PN_(i) (f), that is, afrequency domain pseudo-noise function. Multiplier 140 has as its secondinput, on lead 142, a signal designated w(t), that is, a time domainwindow signal. If, illustratively, PN_(i) (f) is a complex frequencyfunction which has modulus one, and w(t) is of the form w(t)=1 over atime interval of interest, then the square of the magnitude of thefrequency domain characteristic emitted from multiplier 140 is |S(f)|².The square of the magnitude of the frequency domain characteristic ofany time domain signal is generally referred to as the spectrum or thespectral density. Accordingly, by way of terminology, the arrangement ofelements 110-140, 160, and 170 is called the transmitter spectralencoder 101, that is, this spectral encoder 101 generates thetransmitter pulse p_(i) (t).

The code assigned to source 160, which modulates S(f), can be acomplex-valued PN-sequence, generally of the form ##EQU4## where q(f) isa short pulse in the frequency domain of width f_(c). There are a totalof M pulses, and the bandwidth of PN_(i) (f) is Mf_(c). As an example,q(f) can be a rectangular pulse (as will be employed to generate FIG.2); however, other pulse shapes for q(f) can be used to better confinethe energy of the transmitter pulse to the symbol intervals. Forinstance, to obtain one exemplary PN sequence, each sequence element canbe chosen from a set of uniformly spaced points on the unit circle inthe complex plane. Assuming the intended receiver is properlysynchronized with its corresponding transmitter via conventionalsynchronization techniques, then demodulation by the "conjugate" code,in which each PN-sequence element is replaced by its conjugate, enablesdetection of the transmitted data sequence. If, however, the decoder ismatched to a different PN-sequence, then the output signal from thegiven receiver is additive low-intensity interference. Details ofdecoding will be presented shortly.

An example of a ST-CDMA transmitter pulse obtained from a S(f) which isconstant over the normalized frequency interval [-1/2, 1/2] is shown inFIG. 2. The random sequence used to modulate the spectrum has length256. Only 128 sequence elements are chosen randomly, however, since thisrandom sequence and its conjugate modulate the positive and negativehalves of S(f), respectively. This guarantees that p_(i) (t) isreal-valued. The sequence elements a_(k), k=0, . . . , 127, are randomlychosen from the set {1, e^(j)π/2, -1, e^(-j)π/2 }. It is easily verifiedthat this transmitter pulse is given by ##EQU5## where M=256, and f_(c)=1M. It is noted that p(t) is of infinite duration, and therefore in apractical implementation must be truncated in time by a time window suchas device 170 of FIG. 1. In FIG. 1, the signal appearing on lead 131,which corresponds to p(t) of infinite duration, is designated theintermediate time signal.

The inverse Fourier transform operation performed by device 130 inspectral encoder 101 may be implemented in a straightforward manner byconventional surface acoustic wave (SAW) chirp filters. The referenceentitled "Surface Acoustic Wave Devices", published in the IEEECommunications Magazine by Milstein and Das, pages 25-33, September,1979 discusses such conventional implementations.

A second embodiment to implement transmitter 100, as shown in FIG. 3, isto precompute p_(i) (t), as guided by the circuitry and concomitantoperations depicted by spectral encoder 101 of FIG. 1, and thensynthesize filter 330 of FIG. 3 having p_(i) (t) as the impulseresponse. The transmitted time signal, on lead 331, is then the outputof this filter in response to a series of short pulses produced at therate of 1/T by short pulse generator 310, as modulated in modulator 320by data symbols produced by data source 180. These short pulses (whichideally are a series of delta functions) are "spread" in time by such aspectral encoder (hence the origin of the name "spread-time CDMA").

Receiver of the Present Invention

ST-CDMA receiver 400, or "spectral" decoder, shown in FIG. 4 includesthe serial combination of: receiver multiplier 410; Fourier transformer420; conjugate modulator 430; and detector 440. The incoming channelsignal to be processed is received from channel 50 over lead 51. Inorder to restrict signals in the time domain, the incoming channelsignal is multiplied, via multiplier 410, by a receiver time windowsignal w_(R) (t) provided by device 450, and then delivered to signalseparator 415. In effect, the incoming channel signal is partitioned bythe combination of multiplier 410, window 450, and separator 415 into asequence of time signals wherein each partitioned time signal is ofduration T', where T'≧T. (Ideally, T' is the duration of the transmitterpulse). Synchronization for this partitioning is received by window 450from detector 440 over lead 451. Each partitioned time signal isdelivered to Fourier transform device 420 from separator 415 via lead411. Each of these partitioned time signals is converted, one at a time,to a frequency domain representation by Fourier transformer 420 toproduce a frequency domain representation--designated the receivedcharacteristic--for each partitioned time signal. During the conversion,because of the partitioning, each time signal only has values in aninterval of duration T' and is zero elsewhere. The received frequencycharacteristic on lead 421 in response to each transmitted pulseb_(k).sup.(i) p_(i) (t) is b_(k).sup.(i) S(f)H(f)PN_(i) (f) (ignoringthe effect of w_(R) (t). To prepare the received characteristic fordetection within detector 440, the received characteristic is multipliedin multiplier 430 by: frequency characteristic S(f); the conjugate ofthe pseudo-noise source PN_(i) (f), i.e., PN_(i) *(f); and the conjugateto the channel characteristic H(f), i.e., H*(f). Then, the frequencycharacteristic on lead 431 is b_(k).sup.(i) |S(f)|² |H(f)|². Integrator441 then integrates the characteristic on lead 431 over the bandwidthfor which S(f)>0. Since |S(f)H(f)|² ≧ 0 for all frequencies, sampler 445decides if b_(k).sup.(i) =1(-1) whenever the integration is positive(negative). Synchronization of a transmitter-receiver pair isaccomplished via element 443 in any conventional, well-known manner. Thesynchronization signal is provided to integrator 441, sampler 445,receiver time window 450, separator 415 and Fourier transformer 420.Fourier transformer 420 may also be implemented with a surface acousticwave device as set forth in the aforementioned article by Milstein andDas.

The arrangement depicted in FIG. 5 is an alternative embodiment toreceiver 500 realized by matched filter 510. In this arrangement, filter510 has a frequency domain characteristic given by the product of: (a)the conjugate of the Fourier transform of the transmitter pulse, that isp_(i) *(f) where p_(i) (f) is the Fourier transform of p_(i) (t); and(b) H*(f)S(f). The output of filter 510, appearing on lead 511, issampled by sampler 520 to produce the estimates {b_(k).sup.(i) }.Multiplier 505, receiver time window 530, and synchronization device 540are counterparts to elements 410, 450 and 443 in FIG. 4.

Generating the Transmitter Magnitude S(f)

It can be shown that the SIR--the ratio of received signal power toreceived interference power at the output of integrator 441 of FIG.4--is a functional of the square of the magnitude of the transmittercharacteristic, that is, the spectrum of the transmitter pulse. Thus,the spectrum that maximizes the SIR subject to an average transmittedpower constraint can be determined. It is required to ##EQU6## subjectto ##EQU7## where is is assumed that |S(f)|=0 for |f|>W. The SIR can becomputed, and a standard variational argument shows that the optimalspectrum is given by ##EQU8## α=(N₀ T)/[4M(K-1)], and μ=meas B(f), thatis, the range of frequencies over which S(f)>0. Also, N₀ /2 is thevariance of the white noise, K is the number of transmitters, and M isthe length of the PN sequence assigned to each transmitter. It is notedthat c₁ is simply a normalization constant that enforces the constraintof equation (6).

When the additive channel noise is small, i.e., if N₀ /2→0, then c₂ →0and ##EQU9## for all f such that |H(f)|² >>c₂.

EXAMPLE 1

To demonstrate the principles of the present invention with respect to aspecific example, it is supposed that |H(f)|=1 for |f|<W. In thisexample ##EQU10## so that from equation (10), B(f)={f:|f|<W}. In thiscase c₁ =(1+2Wα)/2W, and it is easily verified that ##EQU11## The SIR inthis case can be computed as SIR² =2WT/[(K-1)+N₀ T/(2M)]. The plot ofFIG. 2 already depicted one transmitter pulse for a transmittermagnitude S(f) which was constant over a frequency band, as is thispresent case.

EXAMPLE 2

As a second example, it is assumed that the channel impulse response ish(t)=e^(-t), or |H(f)|² =1/(1+4π² f²). |H(f)|² >c₂ when ##EQU12## sothat from equation (10), μ=meas B(f)=2f₀. From equations (8) and (9), itfollows that ##EQU13## As N₀ /2 increases from zero to infinity, c₂therefore increases from zero to ##EQU14## A plot of optimizedtransmitted spectra |S(f)|² for different values of α is shown in FIG.6. Spectrum generator 110 of FIG. 1 can then generate the appropriateS(f) once a given α is selected.

EXAMPLE 3

As a final, qualitative example, it is supposed that H(f) is composed oftwo ideal bandpass channels each having bandwidth W with respectivesupport on disconnected or separate frequency bands. Since H(f) is even,the total available channel bandwidth is 4 W. The transmitter pulse canbe matched to this channel, which results in essentially the sameperformance as for the case of an ideal bandlimited channel withbandwidth 4 W. Then SIR=[4 WT/(K-1)]^(1/2) in the absence to backgroundnoise. In contrast, a conventional spread-spectrum system would mostlikely treat this channel as two independent channels each havingbandwidth 2 W. An additional channel assignment scheme is then needed toassign users to one of the two independent bandpass channels.

It is to be understood that the above-described embodiments are simplyillustrative of the application of the principles in accordance with thepresent invention. Other embodiments may be readily devised by thoseskilled in the art which may embody the principles in spirit and scope.Thus, it is to be further understood that the methodology andconcomitant circuitry described herein is not limited to the specificforms shown by way of illustration, but may assume other embodimentslimited by the scope of the appended claims.

What is claimed is:
 1. Circuitry in a receiver for spectrally decoding aspectrally encoded transmitted time signal conveying symbols at a symbolrate communicated by a corresponding transmitter and detected on achannel having a channel characteristic and noise interference, thetransmitted time signal being derived from a transmitter pulse having aunique pseudo-noise code assigned to the phase characteristic of thetransmitter pulse, the circuitry comprisingmeans for synchronizing thereceiver to the corresponding transmitter at the symbol rate, means,responsive to said means for synchronizing, for truncating thetransmitted time signal over predetermined time intervals to produce awindowed time signal, and matched filter means, responsive to saidwindowed time signal, for separating said windowed time signal into timesegments and for producing a filter output in correspondence to each ofsaid time segments, said matched filter means having a transfer functiondetermined by the conjugate of the channel characteristic and theconjugate of the frequency domain characteristic of the transmitterpulse.
 2. A method in a receiver for spectrally decoding a spectrallyencoded transmitted time signal conveying symbols at a symbol ratecommunicated by a corresponding transmitter and detected on a channelhaving a channel characteristic and noise interference, the transmittedtime signal being derived from a transmitter pulse having a uniquepseudo-noise code assigned to the phase characteristic of thetransmitter pulse, the circuitry comprisingsynchronizing the receiver tothe corresponding transmitter at the symbol rate, truncating thetransmitted time signal over predetermined time intervals to produce awindowed time signal, separating said windowed time signal into timesegments, and producing a filter output from a matched filter incorrespondence to each of said time segments, the matched filter meanshaving a transfer function determined by the conjugate of the channelcharacteristic and the conjugate of the frequency domain characteristicof the transmitter pulse.